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QJEEM17Ma9c4a: JEE Main 2017 Mathematics - Class 11 JEEM17Ma9c4a Solution: If two parallel chords of a circle, having diameter 4units, lie …

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles cos⁡−1(17){\cos ^{ - 1}}\left( {{1 \over 7}} \right) and sec −- 1 (7) at the center respectivey, then the distance between these chords, is :

Multiple Choice Options

  • A 47{4 \over {\sqrt 7 }}
  • B 87{8 \over {\sqrt 7 }}
  • C 87{8 \over 7}
  • D 167{16 \over 7}

Step-by-Step Verified Solution

JEE Main 2017 (Online) 8th April Morning Slot Mathematics - Circle Question 132 English Explanation

Since cos2 θ\theta = 1/7   ⇒\Rightarrow  2 cos2 Q −- 1 = 1/7

⇒\Rightarrow    2 cos2 θ\theta = 8/7

⇒\Rightarrow     cos2 θ\theta = 4/7

⇒\Rightarrow     cos2 θ\theta = 47{4 \over 7}

⇒\Rightarrow    cos2 θ\theta = 27{2 \over {\sqrt 7 }}

Also, sec2 ϕ\phi = 7 = 12cos⁡2ϕ−1{1 \over {2{{\cos }^2}\phi - 1}} 7

= cos2 ϕ\phi −- 1 = 17{1 \over 7}

= 2 cos2 ϕ\phi = 87{8 \over 7}

= cos ϕ\phi = 27{2 \over {\sqrt 7 }}

P1P2 = r cos θ\theta + r cos ϕ\phi

= 47+47{4 \over {\sqrt 7 }} + {4 \over {\sqrt 7 }} = 87{8 \over {\sqrt 7 }}

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